Lecture17:CellVolumeRegulation
17.1.Introduction
Inlectures15and16,welearntabouttheorganizationandcompositionofthe
cellmembrane,andhowmaterial–ionsandmolecules–moveacrossthecell
membrane.Inthislecture,wewilllearnabouttheforcesthatmovewateracross
thecellmembraneandthecellularmechanismsbywhichcellvolumeiskept
relativelyconstant.
17.2.Objectives
Afterthislecture,weshouldbeableto
1) Statetheforcesthatmovewaterintooroutofthecell.
2) ExplaintheGibbs-DonnaneffectandtheroleoftheNa/KATPasepump.
3) Describethecell’sresponsetoshort-termandlong-termchangesin
extracellularfluidosmolality.
4) Explainthedifferencebetweenosmolalityandtonicity.
5) Describetheeffectonbody’sECFandICFvolumeandosmolalityofthe
additionofisotonicsaline,purewater,5%dextrose(glucose)solution,
andNaCl.
17.3HydrostaticandOsmoticPressures
Theamountofwaterpresentinsidethecelldeterminesitsvolume.Inthis
section,wewilllookattheforcesthatcausemovementofwatermolecules.The
firstishydrostaticpressure.Whenweapplypressuretowater,thewaterwill
movefromaregionofhighhydrostaticpressuretoaregionoflowhydrostatic
pressure.Inourbodies,thereisnohydrostaticpressuredifferencebetweenthe
insideandoutsideofthecell.Sothemovementofwaterintooroutofourcells
doesnotinvolvehydrostaticpressure.Andalso,therearenopumpsinthecell
membraneformovingwaterintooroutofthecell.
Plantcellshaveatough,rigidcellulosewallsurroundingthem.
Therefore,aswatermovesintoaplantcell,theplantcellcan
develophydrostaticforceorpressuretoopposethemovement
ofwaterintoitself.
Theotherpressurethatcancausewatertomoveisosmoticpressure.When
thereisadifferenceinosmoticpressurebetweeninsideandoutsideofthecell,
waterwillmoveeitherintooroutofthecell.Iftheosmoticpressureinsidethe
cellishigherthantheoutside,waterwillmoveintothecell.Andthereversewill
occurwhentheosmoticpressureisgreateroutsidethaninside.Sothe
movementofwatercanmakethecellswellorshrink.
Sowenowknowthattheprimarypressureorforceformovementofwaterinto
oroutofourcellsistheosmoticpressure.
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Theosmoticpressureasolutioncandevelopdependsonthe
totalnumberofparticlesormoleculesorionspresentinthe
solution.Thesizeoftheparticlesisimmaterial.
17.4.Movementofwateracrossthecellmembrane.
Watermoleculescanmoveacrossthephospholipidbilayerofthecellmembrane.
Themorefluidthemembrane,theeasierforwatermoleculestopassthrough.
Thismovementofwaterthroughthelipidbilayerisnotveryfastorlarge.To
increasethemovementofwateracrossthecellmembrane,presentinthecell
membranearewaterchannelscalledaquaporinchannels(APQ).Wewilllearnin
thelecturesonrenalphysiologythatthecollectingductsinourkidneyscan
increasetheamountofAPQchannelsintheircellmembranes.Whenthe
hormoneantidiuretichormone(ADH),alsoknownasvasopressin,ispresent,
APQ2channelsareinsertedintothecellmembraneofthecollectingductcells
allowingincreasedmovementofwateracrosstheircellmembrane.
Whenwatermovesintothecell,itwillcauseittoswellandevencauseitto
burst.Whenwatermovesoutofthecell,thecellwillshrink,andthemolecular
processesinsidethecellwillbeimpaired.Topreventchangesincellvolume,the
osmoticpressuredifferenceacrossthecellmembranehastobekeptatzero,i.e.,
theosmolalityhastobeequalonbothsidesofthemembrane.
Whenwestudytheequationforwatermovementacrossamembrane,
Jv=RT(Osmi–Osmo)
weseethatJv,thefluxofwater(liters/cm2sec)isdirectlyproportionaltothe
differenceinosmoticpressureinsideandoutsidethecell(Osmi–Osmo).(Risthe
UniversalGasConstant,andTisabsolutetemperature).WhenOsmi–Osmo=0,
therewillbenonettmovementofwaterintooroutofthecell.Thevolumeofour
cellswillremainstable.
OsmolarityisOsm/litreH2O;osmolalityisOsm/kgH2O.
Anosmoticpressuredifferenceof1mosm/kgH2Ois
equivalenttoahydrostaticpressureof19.3mmHg.
Thedifferenceinosmoticpressureissymbolicallyexpressed
asΔπ (deltaphi)
Whentherearelargeimpermeantmoleculeslikeproteins,the
osmoticpressureisreferredtoasthecolloidpressureorthe
oncoticpressure.Hydrostaticandoncoticpressureare
importantinthemovementoffluidacrossthebloodcapillary
walls.
Intheglomerulusofthekidneys,fluidismovedbyhydrostatic
forceandformsanultrafiltrateoftheplasma.
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Whatarethetwopressuresorforcesthatinfluencewater
movement?Explainwhyonlyoneofthepressuresorforcesis
theimportantoneforwatermovementacrossamammalian
cell.
Aquaporinchannelsdonotdeterminethedirectionofwater
movement.Theosmoticpressuredifferencebetweenthe
insideandoutsideofthecellwilldeterminethedirectionof
watermovement.
Gibbs-DonnanEquilibrium
Thecellsinourbodyfaceafatalphysiochemicalproblem-theGibbs-Donnan
effect.Ourcellmembranesencloseandareimpermeanttolargemoleculessuch
asproteinsbutarepermeabletoionsandwater.Tounderstandwhatproblem
thiswillcausetoourcells,weneedtostudytheGibbs-Donnaneffectandhowits
potentialfatalconsequenceisprevented.
Wewillstartwithaninitialsituationillustratedinfigure17.1.Herewehavean
intracellular(cytosol)andextracellularcompartmentseparatedbyamembrane
thatisimpermeanttolargenegativelychargedmoleculeslikeproteinsand
phosphates(representedbythesymbolYinthefigure),butpermeanttoNa+,Cl-
andwater.Thisarrangementisquitesimilartothesituationinourbodies.
Figure17.1.Illustrationofaninitialconditionbetweentwocompartments
separatedbyamembranethatisimpermeanttolargenegativelycharged
molecules(symbolY)andpermeabletoNa+,Cl-,andwater.
Wecanseethatthepositiveandnegativechargesareequalinboth
compartments,sothereiselectroneutrality.However,thereisadifferenceinthe
osmolaritybetweenthetwocompartments.Forthepurposeofthisexample,we
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canimaginethattherearenon-chargedmolecules,whicharealsoimpermeant,
inthecytosolcompartment(about149mmol/l).Soourinitialcondition,thereis
nodifferenceintheosmolalitybetweenthecompartments.Andthereisnonett
movementofwatermoleculesacrossthemembrane.
NowwecanstudytheGibbs-Donnaneffectandhowitwillreachanequilibrium
–theGibbs-Donnanequilibrium.WhiletheconcentrationofNa+isthesamein
bothcompartments,theCl-concentrationisnotthesameinbothcompartments;
itisgreaterintheextracellularsidethanthecytosol.
Weknowthatwhenthereisconcentrationdifference,therewillbeamovement
ofmoleculesorionsfromthesidewiththehigherconcentrationtothesidethat
hasalowerconcentration.Inthiscase,Cl-willmovefromtheextracellularspace
intothecytosolspaceduetoitsconcentrationdifference.AsCl-movesintothe
cytosolspace,itwillincreasethenegativechargeincytosolspace,andthiswill
attractNa+intothecytosolspace.Infigure17.2,thedifferenceinchargeis
shownbyplusandminussigns.Sooverall,therewillbeanettmovementofCl-
andNa+intothecytosolspace,ineffectmovementofNaClfromextracellular
spaceintothecytosolspace.
Letusconsiderthesituationafter10mMofNaClhasmovedintothecytosol
space.Thisisshowninfigure17.2.
Figure17.2.Thesituationafter10mMofNaClhasmovedintothecytosolspace
fromtheextracellularspace.
Nowwhenweconsidertheintermediatestateshowninfigure17.2,theelectrical
andchemicalgradientsofNa+andCl-arenotequal,andmovementofNaClinto
thecellwillcontinueuntilastateofequilibriumisreached.
Inthemodelwearediscussing,equilibriumwillbeachievedwhenthereisan
electricpotentialdifferenceof18.4mVacrossthemembrane.Atthisstageboth
Na+andCl-areattheirrespectiveelectrochemicalequilibrium.Thisisshownin
figure17.3.
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Figure17.3.ThefinalstateatGibbs-Donnanequilibriumandconcentration
differencedbetweentheextracellularandcytosolicspace.Ψisthesymbolfor
electricpotential,andPistheosmoticpressuredevelopedbytheinflowofNaCl.
Studyingfigure17.3.,wecanseethatthesumoftheionsandthelarge
impermeantmoleculeinthecytosolspaceisgreaterthanintheextracellular
space.Thetotalis200mMfortheextracellularspaceand251mMforthe
cytosolicspace.Therefore,thisdifferenceinthenumberofparticlesormolecules
willcreateabigosmoticpressuredifference,andaswerecallosmoticpressure
differencewillcausemovementofwater(osmosis).Sowaterwillmovefrom
extracellularspaceintothecytosolicspace.Fortunately,inourexample,the
cytosolicspaceissurroundedbyrigidwalls,andwatercannotmoveinbecause
thereisnospaceforit.Thecytosolicspacewillnotswell.Insteadapressurewill
developtoopposetheosmoticgradient.Inourexample,thispressureis967mm
Hg(1.3atmospheres).
Rememberthatamolerepresentsthenumberofparticles,
moleculesorionspresent.Onemolecontains6x1024numberof
particles,moleculesorions.Itisthesameasusingtheterma
dozentorepresent12orabaker’sdozenfor13.
Butwhataboutourcells?Ourcellsdonothaverigidwallsandaresubjecttothe
Gibbs-Donnaneffect.Therefore,waterwillmoveintoourcells,andtheywill
startswellingandburst,andwewilldie.Sowhyisthisnothappeninginour
bodies?Inthenextsection,wewilllearnabouttheevolutionarydevelopmentof
themechanismthatpreventsthefatalconsequenceoftheGibbs-Donnaneffect
fromoccurring.
Tosummarize,inthispartofthelecture,wehavelearntthataswearemakeup
ofcellsthatencloseimpermeantchargedmoleculesbutarepermeanttoions,
andthereforeGibbs-Donnaneffectmusttakeplace.
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OntheleftisFrederickGeorgeDonnan,CBEFRS(6September
1870–16December1956)whowasanIrishphysicalchemist
knownforhisworkonmembraneequilibria,and
commemoratedintheDonnanequilibriumdescribingionic
transportincells.HespentmostofhiscareeratUniversity
CollegeLondon.OntherightisthegreatJosiahWillardGibbs
(February11,1839–April28,1903),anAmericanscientist
whomadeimportanttheoreticalcontributionstophysics,
chemistry,andmathematics.Hisworkontheapplicationsof
thermodynamicswasinstrumentalintransformingphysical
chemistryintoarigorousdeductivescience.Togetherwith
JamesClerkMaxwellandLudwigBoltzmann,hecreated
statisticalmechanics(atermthathecoined),explainingthe
lawsofthermodynamicsasconsequencesofthestatistical
propertiesoflargeensemblesofparticles.Gibbsalsoworked
ontheapplicationofMaxwell'sequationstoproblemsin
physicaloptics.Asamathematician,heinventedmodern
vectorcalculus(independentlyoftheBritishscientistOliver
Heaviside,whocarriedoutsimilarworkduringthesame
period).https://en.wikipedia.org/wiki/Main_Page
Sodium-PotassiumATPasepump.
TopreventtheinevitableconsequenceoftheGibbs-Donnaneffectfrom
occurring,ourcellmembraneshavebeenmade“impermeable”toNa+ions.The
termimpermeableisputinquotationmarksasthemembraneisnot
impermeabletoNaionsbutappearstobeso.Thisfunctionalimpermeabilityof
ourcellmembranestoNa+isduetotheactivityoftheNa/KATPasepump.This
pumppumpsout3Na+outofthecelland2K+intothecell.SoastheNa+enters
thecell,itispumpedout,effectivelymakingthemembraneseem‘impermeable’
toNa.IfwestoptheNa/KATPasepumpbyusingatoxin,ouabin,ourcellswill
startswellingbecausetheGibbs-Donnaneffectwillnowcontinuetowardsits
equilibrium.ThesamewillalsooccurtoourcellswhenATPproductiondeclines
orstops.Thus,thecrucialfunctionoftheNa/KATPasepumpistopreventthe
accumulationofNa+inourcellsandprevent,andsopreventsariseinthecell’s
osmolality.
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Inthisshortsection,wehavelearnttheimportanceoftheNa/KATPasepumpin
theregulationofcellvolume;howinthecourseofevolutionandforlifeformsto
existonthisplanet,asolutionhadtofoundforthefataleffectoftheGibbsDonnaneffect;thiswastheNa/KATPasepump.
Thecell’sresponsetoshorttermandlongtermvolumechanges.
OurcellshavemechanismstocounteracutechangesinECFosmolality.IftheECF
increases,thiswillcreateanosmoticgradientandwaterwillmovefromthecell
intotheECFandcauseourcellstoshrink.Tobringthecellvolumebacktoits
normalvolume,ourcellhastoincreaseitsosmolalitytomatchthatoftheECF.
ThisitwilldobyincreasinginflowofNaandCl.
Ifontheotherhand,theECFosmolalitydecreasescomparedtothecellsthan
waterwillmovedownitsosmoticgradientintoourcellscausingthemtoswell.
Topreventthischangeincellvolume,ourcellswillhavetoincreaseoutflowof
K+andCl-soitsosmolalitydecreasesandthecellvolumereturnstonormal.
These mechanisms are called the Volume Regulatory Increase (RVI) and
VolumeRegulatorDecrease(RVD),respectively.
IftheincreaseinECFosmolalityislong-term,ourcellswillincreaseits
osmolalitytomatchthatoftheECFbyaccumulatingorganicsolutesespecially
sorbitolandinositol.
Thedifferencebetweenosmolalityandtonicity
Inthissection,wewilllearnthedifferenceinmeaningofthetermsosmolality
andtonicity.Thisdistinctionisimportantforustounderstandasitunderliesthe
principleoffluidreplacementtherapyinhealthcarepractice.
Tounderstandthis,letustaketwoexamples.
Inthefirstexample,westudytheeffectofaddingmannitoltotheECF.Theinitial
effectwillbeanincreaseinECFosmolalityandwaterwillmoveoutofourcells
andshrinkinvolume.Asmannitolisanimpermeantmolecule,theonlywayfor
ourcellstorestoretheircellularvolumeistooperatetheirRVImechanism;
otherwisetheywillremaininashrunkenstate,andtheirbiochemicalmachinery
willbeimpaired.
Inthenextexample,weaddureatotheECF.Aswiththemannitol,theECF
osmolalitywillincreaseinitially,andwaterwillmoveoutofourcellscausing
themtoshrink.
Butasureaisapermeablemolecule,i.e.,itcandiffuseacrossthecellmembrane,
itwilldiffuseintothecelluntilitsconcentrationisequalonbothsidesofthecell
membrane.Thismovementofureawillincreasethecell’sosmolalityandmakeit
equaltothatoftheECF.Andthecellvolumewillreturntonormal.
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Sonowweknowthatthedifferencebetweenisosmoticandisotonicsolutionsis
thatisotonicsolutionsdonotcauseachangeincellvolume;theireffective
osmolalityisthesameastheICF.
Whenasolutionisdescribedusingosmolalitythecontribution
ofalltheparticlesinthatsolutionisconsidered.Whena
solutionisdescribedusingtonicity,thecontributionofthe
permeantparticleinthesolutionisexcluded,i.e.,onlyits
effectiveosmolalityisdescribed.
Weuseisotonicsolutionsforintravenoustherapyfortreatmentofpatients.For
example,tohydrateadehydratedperson,wecannotintroducepurewaterinto
thebodythroughavein(intravenoustherapy,IV,figure17.4).Theadditionof
purewaterwillcausetheosmolalityoftheplasmatodecreasesharply,and
waterwillflowintothebloodcellsaswellastheepithelialcellsliningthevein
causingthemtoswellandburst.Toovercometheeffectofasharpchangein
osmolality,wegive5%dextrose(glucose)solutionIV.Bythisapproach,the
osmoticshockispreventedastheosmolalityof5%dextrosesolutionisthesame
asthatoftheECF.
Figure17.4.Apersonreceivingasolutionintravenously.
(https://en.wikipedia.org/wiki/Intravenous_therapy#/media/File:ICU_IV_1.jpg)
Butasthedextrosewillbemetabolizedbythecellsofourbody,wewillhave
effectivelyincreasedourtotalbodywater.
Kidneyfailureresultsinariseinbodyurea,butthatdoesnot
changetheECFtonicitybecauseureaisapermeantmolecule.On
theotherhand,anincreaseinglucose(hyperglycemia)will
increasethetonicityofECF(hypertonia)andcausewaterto
moveoutofthecellscausingthecellstoshrink.
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DescribetheeffectonECFandICFvolumeandosmolalityof
adding(a)1.5lisotonicsaline,and(b)1.5lpurewater.
Itisimportantthatyouattempttoanswerthisquestionbefore
youreadthenextsection.
TheeffectonECFandICFoftheadditionof(1)isotonicsaline,(2)pure
water,or(3)pureNaCl.
Letustakeeachcase.
When1.5lofisotonicNaClistransfused,IV,intoourbodies,ourECFvolumewill
increaseby1.5l.ButasnoosmoticgradientwilldevelopbetweenourECFand
ICF,therewillbenowatermovementintotheICFandnochangeintheICF
volume.IsotonicNaClisa9%NaClsolution.
Whenwedrink1.5lofwaterorhavetransfused1.5l5%dextrose(glucose)
solution,itwillcausetheosmolalityoftheECFtodecreasefrom290mosm/land
anosmoticgradientbetweentheECFandICFwillbecreated.Waterwillmove
intothecellsuntiltheosmolalityoftheECFandICFareequal.Sohowwillthe
osmolalityandvolumechangeintheECFandICF?
Inourstandard70kgadultmale,totalbodywateris42l(60%ofbodyweight).
25LispresentinICFand17LintheECF.Theoverallosmolalityis290mOsm/l.
SobeforethewaterwasaddedthetotalosmolalityoftheECFwas290mOsm/lx
17l=4,930mOsm.When1.5litersofwaterisadded,thevolumeofourECF
increased.Itbecome17+1.5=18.5l.SothenewosmolalityofourECFwillnow
be4,930mOsm/18.5l=266.5mOsm/l.
NowthatourECFosmolalityislessthanourICFosmolality,waterwillmoveinto
thecells.OurECFvolumewilldecrease,andtheICFvolumewillincreaseand
withthattheosmolalityofourICFwilldecrease.
Howwilltheinfusionof1.5lwaterdistributeitselfbetweentheECFandICF?As
ourECFmakesup40%ofthebodywater,40%ofthe1.5lwillremaininour
ECF.SothefinalvolumeofourECFwillbe17L+(1.5x0.4L)=17.6L.Andits
osmolalitywillnowbe4,930mOsm/17.6l=280.8mOsm/l.
AsICFmakesup60%ofourbodywater,60%of1.5lofwater(0.9l)willmove
intoourcells.OurICFwillexpandby0.9lto25.9l(25l+0.9l).Theadditionof
waterwilldecreaseitsosmolality.WhatwillbetheosmolalityofourICFnow?
Beforethewaterinfusion,thetotalosmolalityofourICFwas290mOsm/lx25l
=7,250mOsm.NowthatthereisanincreaseinourICFvolumeto25.9l,the
osmolalityofourICFwillnowbe7,250mOsm/25.9l=279.9mOsm/l.
SowhenwaterisaddedintothebodyboththevolumeandosmolalityofourICF
andECFwillchange.
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Usethesamereasoningshowninthetwoexamplesaboveto
workouthowtheECFandICFvolumesandosmolalitywill
changewhenNaClequivalentto435mOsmisaddedtothe
body.
Fromtheaboveexamples,wehavelearntacrucialpoint,namelythatwhole
bodyNa+determinestheECFvolumewhiletotalbodywaterdeterminesthe
body’sosmolality.
Summary
Wehavelearntinthislecturethattheamountofwaterpresentinsideourcells,
theintracellularcompartment,andoutsidethecells,theextracellular
compartment,hastothebesame.Thatistoensurethatthereisnodifferencein
osmolalityacrossthecellmembrane.However,duethecellularcompositionof
ourbodies,thereisaphysiochemicaleffect,theGibbs-Donnaneffect,whichifnot
circumventedwillresultinourcellsexploding.WelearntthattheNa/KATPase
pumpisvitalinensuringthattheGibbs-Donnaneffectcannotbeallowedto
reachequilibrium.Usingourunderstandingofthedifferencebetweenosmolality
andtonicity,welearnttherationalefortheuseofintravenoustherapy.
Activity
Modelexaminationquestion
Recommendedreading
WalterF.BoronandEmileL.Boulpaep.MedicalPhysiology:ACellularand
MolecularApproach.(2012).Chapter3.SaundersElsevier
References
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